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Algorithm Wrapup Sub-sample O(log 1/ε) times in powers of 2 In each level of sub-sampling maintain CountSketch with O~(1/ε 1/2 ) buckets Find as many heavy coordinates as you can! Intuition: if CountSketch fails, there are many heavy elements that can be found by sub-sampling Wouldnt work for CountMin as bucket error could be ε because of n-1 items each of value ε/(n-1)

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Rounding Matrices [DIPW] A is a matrix of real numbers Can assume orthonormal rows Round the entries of A to O(log n) bits, obtaining matrix A Careful –Ax = A(x+s) for small s –But s depends on A, no guarantee recovery works –Can be fixed by looking at A(x+s+u) for random u